In a medium saucepan, stir together the cold water, chickpea flour, salt and pepper. Bring the mixture to a boil over medium-high heat, stirring often to prevent lumps from forming. Cook until the mixture is very thick and starts pulling away form the sides of the pan, 15- 20 minutes. A wooden spoon should easily stand straight up unassisted in the dough when it is cooked enough.

Spread the hot chickpea flour onto a lightly greased wooden cutting board or baking sheet. Cool to room temperature. And cut into 2" squares. (These squares can be kept airtight in the refrigerator for up to a week at this point with little effect.)

In a large bowl, combine the mashed potatoes, Parmesan Cheese, egg, egg yolk, parsley, salt and pepper. Dampen your hands with water and shape the croquettes into 16 1"x 3" oval croquettes.

Heat at least 1 inch of oil in a wide, deep sided sauté pan over medium high heat ( 375). Fry the chickpea squares in the hot oil a few at a time until they are brown, crisp and puffy (2 minutes). Drain on paper towels and sprinkle with salt. Roll the croquettes in the bread crumbs and fry a few at a time in the hot oil until golden brown and heated through, 2-3 minutes. Drain well on paper towels. Repeat with the remaining ingredients

Place 3-4 chickpea fritters and 2 potato croquettes in a sliced bun and serve immediately.